Deflection of light with the equivalence principle
Degree GrantorUniversity of Canterbury
Degree NameMaster of Science
A thorough treatment of the Strong Equivalence Principle is presented, demonstrating its failure in dealing with non-uniform gravitational fields. In particular, a calculation utilising the equivalence principle is shown to produce an incorrect rate of deflection of light. This calculation is used as a tool to investigate the nature of this deflection, and the meaning of the Strong Equivalence Principle. Using a generalised metric for outside a static, spherically symmetric gravitational source, it is shown that the failure of the equivalence principle is geometric and not due to any particular choice of metric. When transformed into a displaced rectangular coordinate system, the generalised metric consists of both diagonal and off-diagonal elements. Only the diagonal elements are equivalent to a flat, uniformly accelerating frame. The off-diagonal elements produce non-zero elements in the Riemann Curvature Tensor and are thus attributed to curvature. Therefore, the Strong Equivalence principle is only valid in the weak field limit, where the components of the Riemann curvature tensor vanish. In this case the metric becomes flat, which is the equivalent of a uniform gravitational field. Using the Schwarzschild metric in displaced rectangular coordinates, the effect of curvature on the rate of deflection of light are determined by tracing the effect of the off-diagonal elements. This calculation shows that only one-third of the deflection rate is due to acceleration in the local inertial frame, with the remaining two-thirds being the result of curvature. Because the rate of deflection is is an infinitesimal quantity defined locally, this shows the effects of curvature are important even for local measurements.